x^3 + y^3 = (x + y)(x^2 - xy + y^2) を使って

27000001 = 27⋅10^6 + 1
= (3⋅10^2)^3 + 1^3
= (3⋅10^2 + 1){(3⋅10^2)^2 - 3⋅10^2 + 1}
= (3⋅10^2 + 1){(3⋅10^2 + 1)^2 - 9⋅10^2}
= (3⋅10^2 + 1)(3⋅10^2 + 1 - 3⋅10)(3⋅10^2 + 1 + 3⋅10)
= 301⋅271⋅331
= 7⋅43⋅271⋅331